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Show the Proof

In [1]:
import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof
Out[1]:
 step typerequirementsstatement
0instantiation1, 2, 3, 4, 5, 6, 7, 8, 9, 10*  ⊢  
  : , : , : , : , : , :
1reference14  ⊢  
2reference15  ⊢  
3reference43  ⊢  
4reference17  ⊢  
5instantiation24  ⊢  
  : , :
6instantiation24  ⊢  
  : , :
7reference20  ⊢  
8reference23  ⊢  
9reference19  ⊢  
10instantiation26, 11, 12  ⊢  
  : , : , :
11instantiation31, 13  ⊢  
  : , : , :
12instantiation14, 15, 43, 16, 17, 18, 23, 19, 20, 21*  ⊢  
  : , : , : , : , : , :
13instantiation22, 23  ⊢  
  :
14theorem  ⊢  
 proveit.numbers.addition.association
15axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
16theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
17theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
18instantiation24  ⊢  
  : , :
19instantiation46, 37, 25  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
21instantiation26, 27, 28  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.addition.elim_zero_left
23instantiation46, 37, 29  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
25instantiation46, 41, 30  ⊢  
  : , : , :
26axiom  ⊢  
 proveit.logic.equality.equals_transitivity
27instantiation31, 32  ⊢  
  : , : , :
28instantiation33, 34  ⊢  
  :
29instantiation46, 41, 35  ⊢  
  : , : , :
30instantiation46, 44, 36  ⊢  
  : , : , :
31axiom  ⊢  
 proveit.logic.equality.substitution
32theorem  ⊢  
 proveit.numbers.numerals.decimals.add_2_3
33theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
34instantiation46, 37, 38  ⊢  
  : , : , :
35instantiation46, 44, 39  ⊢  
  : , : , :
36instantiation46, 47, 40  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
38instantiation46, 41, 42  ⊢  
  : , : , :
39instantiation46, 47, 43  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
42instantiation46, 44, 45  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
45instantiation46, 47, 48  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat5
*equality replacement requirements